Resampling from the past to improve on MCMC algorithms

Abstract: We explore two strategies that resample from previously sampled observations in a Markov Chain Monte Carlo algorithm. In one strategy the MCMC sampler reuses its own past. We show that in general this strategy generates a sampler with slower mixing. We propose another strategy based on multiple chains where some of the chains reuse past samples generated by other chains. This latter algorithm is related to the Equi-Energy sampler of [11]. We show by examples that this strategy yields a viable Monte Carlo methods with mixing properties similar to those of the Equi-Energy sampler. AMS 2000 subject classifications: Primary 60C05, 60J27, 60J35, 65C40.